;;;数据抽象
;;;        use
;;;========================
;;;  abstraction barrier
;;;========================
;;;     representation
;;;
 
;;;水平屏障：数据抽象
;;;垂直屏障：抽象的不同实现(不同表示representation)
 
;;;复数：实数部分和虚数部分
;;;两种表示方式：一种是xy坐标，一种是距离原点的距离和角度
 
;;;arithmetic operations on complex numbers
;;;复数的加减乘除
(define (+c z1 z2) ... )
(define (-c z1 z2) ... )
(define (*c z1 z2) ... )
(define (/c z1 z2) ... )
 
 
;;;selectors
(real-part z)
(imag-part z)
(magnitude z)
(angle z)
 
;;;constructors
(make-rectangular x y)
(make-polar r a)
 
 
;;;加减使用直角坐标形式
;;;乘除使用极坐标形式
(define (+c z1 z2)
  (make-rectangular
   (+ (real-part z1) (real-part z2))
   (+ (imag-part z1) (imag-part z2))))
 
(define (-c z1 z2)
  (make-rectangular
   (- (real-part z1) (real-part z2))
   (- (imag-part z1) (imag-part z2))))
 
(define (*c z1 z2)
  (make-polar
   (* (magnitude z1) (magnitude z2))
   (+ (angle z1) (angle z2))))
 
(define (/c z1 z2)
  (make-polar
   (/ (magnitude z1) (magnitude z2))
   (- (angle z1) (angle z2))))
 
;;;我们完成了使用的部分，现在该考虑表示的部分了
;;;we've done the use, let's worry about the representation
 
;;;representing complex numbers as pairs real-part imaginary-part
(define (make-rectangular x y)
  (cons x y))
 
(define (real-part z)
  (car z))
 
(define (imag-part z)
  (cdr z))
 
(define (make-polar r a)
  (cons (* r (cos a)) (* r (sin a))))
 
(define (magnitude z)
  (sqrt (+ (square (car z))
           (square (cdr z)))))
 
(define (angle z)
  (atan (cdr z) (car z)))
 
;;;representing complex numbers as pairs magnitude, angle
(define (make-polar r a)
  (cons r a))
 
(define (magnitude z)
  (car z))
 
(define (angle z)
  (cdr z))
 
(define (make-rectangular x y)
  (cons (sqrt (+ (square x) (square y)))
        (atan y x)))
 
(define (real-part z)
  (* (car z) (cos (cdr z))))
 
(define (imag-part z)
  (* (car z) (sin (cdr z))))
 
;;;对应的层级结构
;;;
;;;  +c -c *c /c (use)
;;;=============================
;;; real-part imag-part mag ang
;;;=============================
;;;            |垂|
;;;            |直|
;;;   rect     |屏|    polar
;;;            |障|
;;;
 
 
;;; typed data
;;; 带类型的数据
;;; type + contents
 
 
;;;support machanism（机制） for manifest（显示） types
(define (attach-type type contents)
  (cons type contents))
 
(define (type datum)
  (car datum))
 
(define (contents datum)
  (cdr datum))
 
;;;type predicates
(define (rectangular? z)
  (eq? (type z) 'rectangular))
 
(define (polar? z)
  (eq? (type z) 'polar))
 
;;;rectangular package
(define (make-rectangular x y)
  (attach-type 'rectangular (cons x y)))
 
(define (real-part-rectangular z)
  (car z))
 
(define (imag-part-rectangular z)
  (cdr z))
 

(define (real-part z)
  (cond ((rectangular? z) ... )
        ((polar? z) ... )))
 
(define (real-part z)
  (cond ((rectangular? z)
         (real-part-rectangular (contents z)))
        ((polar? z)
         (real-part-polar (contents z)))))
 

;;;基于表格的分派
;;;
;;;          |    polar            |     rect
;;;==================================================
;;;real-part |real-part-polar      |  real-part-rect
;;;==========|=======================================
;;;imag-part |imag-part-polar      |  imag-part-rect
;;;==========|=======================================
;;;mag       |mag-polar            |  mag-rect
;;;==========|=======================================
;;;angle     |angle-polar          |  angle-rect
;;;==================================================
;;;
;;;
 
;;;有对这个表格的数据抽象
(put key1 key2 value)
(get key1 key2)
 
;;;installing the rectangular operations in the table
(put 'rectangular 'real-part real-part-rectangular)
(put 'rectangular 'imag-part imag-part-rectangular)
(put 'rectangular 'magnitude magnitude-rectangular)
(put 'rectangular 'angle angle-rectangular)
 
;;;installing the polar operations in the table
(put 'polar 'real-part real-part-polar)
(put 'polar 'imag-part imag-part-polar)
(put 'polar 'magnitude magnitude-polar)
(put 'polar 'angle angle-polar)
 
(define (operate op obj)
  (let ((proc (get (type obj) op)))
    (if (not (null? proc))
        (proc (contents obj))
        (error "undefined op"))))
 
;;;defining the selectors using operate
;;;选择函数不再直接实现，而是通过operate来实现
;;;添加一层抽象屏障
(define (real-part obj)
  (operate 'real-part obj))
(define (imag-part obj)
  (operate 'imag-part obj))
(define (magnitude obj)
  (operate 'magnitude obj))
(define (angle obj)
  (operate 'angle obj))
 
 
;;;选择函数
;;;========
;;;contents
 
 
;;;选择函数
;;;========
;;; type
;;;========
;;;contents
 
 
;;; 选择函数
;;;================
;;;   operate
;;;================
;;;   type 
;;;================
;;;   contents
 
;;;由内容加上type，再加上operate过程组成
;;;data-directed programming
 
 
;;;  ADD SUB MUL DIV
;;;====================================================================================
;;;         | 带类型的复数    |              |
;;;         |('complex      |
;;;         | ('rect (2 3)))|
;;;====================================================================================
;;; 有理数   |复数+c -c ...   | 原始的        | polynomials
;;;rational |   complex     | 也就是内置的   |============================================
;;;+rat     |===============| lisp的+-*/    |rational|complex    |original|polynomials
;;;*rat     |      |        |              |         |===========|        |
;;;         | rect | polar  |              |         |rect |polar|        |
;;;         |      |        |              |         |     |     |        |
;;;
;;;
 
;;;带类型的复数
;;;('complex ('rect (2 3)))
;;;带类型的有理数
;;;('rational (2 3))
 
(put 'complex 'add +c)
 
 
;;;rational number arithmetic有理数
;;;有理数程序包还是跟刚才一样，完全不需要修改
(define (+rat x y)
  (make-rat (+ (* (numer x) (denom y))
               (* (denom x) (numer y)))
            (* (denom x) (denom y))))
(define (-rat x y)
  ... )
(define (*rat x y)
  ... )
(define (/rat x y)
  ... )
 
 
;;;如何把以前的有理数程序包安装到刚才的通用运算系统中（*******重点*******）
;;;installing rational numbers in the generic arithmetic system
;;;给有理数加上标签
;;;然后将有理数的运算添加进表里面
(define (make-rat x y)
  (attach-type 'rational (cons x y)))
 
(put 'rational 'add +rat)
(put 'rational 'sub -rat)
(put 'rational 'mul *rat)
(put 'rational 'div /rat)
 
;;如何应用这个系统
(define (add x y)
  (operate-2 'add x y))
 
(define (operate-2 op arg1 arg2)
  (if (eq? (type arg1) (type arg2))
      (let ((proc (get (type arg1) op)))
        (if (not (null? proc))
            (proc (contents arg1) (contents arg2))
            (error "Op undefined on type")))
      (error "Args not same type")))
 
 
;;;如何把多项式添加进去
;;;(polynomial x <term-list>)
;;;x^15 + 2*x^7 + 5
;;;((15 1) (7 2) (0 5))
 
;;;installing polynomials
;;;给多项式添加标签
(define (make-polynomial var term-list)
  (attach-type 'polynomial (cons var term-list)))
 
(define (+poly p1 p2)
  (if (same-var? (var p1) (var p2))
      (make-polynomial (var p1)
                       (+terms (term-list p1)
                               (term-list p2)))
      (error "polys not in same var")))
 
(put 'polynomial 'add 'poly)
 
(define (+terms l1 l2)
  (cond ((empty-termlist? l1) l2)
        ((empty-termlist? l2) l1)
        (else
         (let ((t1 (first-term l1))
               (t2 (first-term l2)))
           (cond
             ((> (order t1) (order t2)) ... )
             ((< (order t1) (order t2)) ... )
             (else ... ))))))
 
((> (order t1) (order t2))
 (adjoin-term t1
              (+terms (rest-terms l1) l2)))
 
((< (order t1) (order t2))
 (adjoin-term t2
              (+terms l1 (rest-terms l12))))
      
;;;矩阵的加减乘除
 
;;;总结:
;;;数的表示方式：
;;;1.基于类型的分派
;;;给数添加上类型，根据不同的类型，进行不同的处理
;;;复数的加减乘除，根据不同的类型，进行不同的处理
;;;然后add根据不同类型转换为不同的处理
;;;抽象层（或者叫抽象屏障）：构造函数、选择函数
;;;
;;;ADD SUB MUL DIV 根据不同的数据类型进行不同的处理
;;;==========================================
;;;复数添加复数的标识
;;;====================================
;;;复数的加减乘除，根据不同的类型进行不同的处理
;;;=========================
;;;带类型的复数
;;;=========================
;;;复数的内容
;;;
;;;问题是：
;;;  +c -c *c /c (use)
;;;=============================
;;; real-part imag-part mag ang （这一层总是需要修改）
;;;=============================
;;;            |垂|
;;;            |直|
;;;   rect     |屏|    polar
;;;            |障|
;;;
;;;
;;;有几层垂直屏障，就有几种标签
;;;第一层垂直屏障，用于区分rect还是polar
;;;第二层垂直屏障，用于区分有理数、复数、基本数据、表达式
;;;
;;;有理数--引出-->抽象屏障
;;;复数---引出--->垂直屏障
;;;
;;;
;;;2.基于表格的分派
;;;统一通过最上层的add sub mul div进行操作
;;;直角坐标
(put 'rectangular 'real-part real-part-rectangular)
(put 'rectangular 'imag-part imag-part-rectangular)
(put 'rectangular 'magnitude magnitude-rectangular)
(put 'rectangular 'angle angle-rectangular)
;;;极坐标
(put 'polar 'real-part real-part-polar)
(put 'polar 'imag-part imag-part-polar)
(put 'polar 'magnitude magnitude-polar)
(put 'polar 'angle angle-polar)
;;;复数运算
(put 'complex 'add +c)
;;;有理数运算
(put 'rational 'add +rat)
(put 'rational 'sub -rat)
(put 'rational 'mul *rat)
(put 'rational 'div /rat)
;;;基本数据
;;;表达式
 